Data hiding is an important way of realising copyright protection for multimedia. In this study, a new predictive method is proposed to enhance the histogram-based reversible data hiding approach on grey images. In those developed histogram-based reversible data hiding approaches, their drawbacks are the number of predictive values less to the number of pixels in an image. In these interleaving prediction methods, the predictive values are as many as the pixel values. All predictive error values are transformed into histogram to create higher peak values and to improve the embedding capacity. Moreover, for each pixel, its difference value between the original image and the stego-image remains within ±1. This guarantees that the peak signal-to-noise ratio (PSNR) of the stego-image is above 48 dB. Experimental results show that the histogram-based reversible data hiding approach can raise a larger capacity and still remain a good image quality, compared to other histogram-based approaches.